Tapping a card with an effect like this will never pay the cost of an ability. For example, tapping a land with this card will not put mana into a player’s pool.

10/4/2004

Icy Manipulator can’t be used to stop someone from using an ability of the permanent you plan to tap. It can be used to make a player use the ability now or to not use it.

10/4/2004

The ability can target a tapped card, but tapping a tapped card does nothing useful. And it will not trigger “if the card becomes tapped” effects.

10/4/2004

If you want to stop someone from attacking with a creature by using this card, you must do so before attackers are declared. You can’t wait until after attackers are declared and then try to use it to make a creature stop attacking. Note that your opponent can’t start declaring attackers without letting you use the Icy Manipulator.

10/4/2004

Tapping an attacking creature which did not tap to attack does not remove the creature from the attack or cause the creature to stop dealing damage.